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We show that critical points of this energy are H\\\"older continuous.\n  As a special case, for $s = 1$, we obtain a new, more stable proof of Fuchs and Strzelecki's regularity result of $n$-harmonic maps into the sphere, which is interesting on its own."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1404.0913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-03T14:05:18Z","cross_cats_sorted":[],"title_canon_sha256":"638496982b05b3ca45192454a40e6f01850518868f3c6b587bae122fdf6f844a","abstract_canon_sha256":"a1db4b422bed138f25528fbfa6e9fcf04084c7683b8a76ba81603f4b979b7a6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:55.051517Z","signature_b64":"+o96I0r4/OSjxyhDmq21QiagnkmPV9mEnTGYUCcMJsFOAEqpz2yTM9yj1ArgRn7t2ppV2yp/5xMqrngo+E0ZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d0aa1da5afa712e017f526ab0a146845f2ba3a9248bfe1be15a5acd8baedef1","last_reissued_at":"2026-05-18T02:54:55.051007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:55.051007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lp-gradient harmonic maps into spheres and SO(N)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Schikorra","submitted_at":"2014-04-03T14:05:18Z","abstract_excerpt":"We consider critical points of the energy $E(v) := \\int_{\\mathbb{R}^n} |\\nabla^s v|^{\\frac{n}{s}}$, where $v$ maps locally into the sphere or $SO(N)$, and $\\nabla^s = (\\partial_1^s,\\ldots,\\partial_n^s)$ is the formal fractional gradient, i.e. $\\partial_\\alpha^s$ is a composition of the fractional laplacian with the $\\alpha$-th Riesz transform. We show that critical points of this energy are H\\\"older continuous.\n  As a special case, for $s = 1$, we obtain a new, more stable proof of Fuchs and Strzelecki's regularity result of $n$-harmonic maps into the sphere, which is interesting on its own."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0913","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.0913","created_at":"2026-05-18T02:54:55.051081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.0913v1","created_at":"2026-05-18T02:54:55.051081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0913","created_at":"2026-05-18T02:54:55.051081+00:00"},{"alias_kind":"pith_short_12","alias_value":"RUFKDWS27JYS","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RUFKDWS27JYS4AL7","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RUFKDWS2","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR","json":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR.json","graph_json":"https://pith.science/api/pith-number/RUFKDWS27JYS4AL7KJVLBIKGQR/graph.json","events_json":"https://pith.science/api/pith-number/RUFKDWS27JYS4AL7KJVLBIKGQR/events.json","paper":"https://pith.science/paper/RUFKDWS2"},"agent_actions":{"view_html":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR","download_json":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR.json","view_paper":"https://pith.science/paper/RUFKDWS2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.0913&json=true","fetch_graph":"https://pith.science/api/pith-number/RUFKDWS27JYS4AL7KJVLBIKGQR/graph.json","fetch_events":"https://pith.science/api/pith-number/RUFKDWS27JYS4AL7KJVLBIKGQR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR/action/storage_attestation","attest_author":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR/action/author_attestation","sign_citation":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR/action/citation_signature","submit_replication":"https://pith.science/pith/RUFKDWS27JYS4AL7KJVLBIKGQR/action/replication_record"}},"created_at":"2026-05-18T02:54:55.051081+00:00","updated_at":"2026-05-18T02:54:55.051081+00:00"}